Fractal and Fractional, Volume 6, Issue 1

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant $H_3\left(1\right)$ for this subclass by applying the Carlson–Shaffer operator to it....

Considering the performance requirements in actual applications, a look-up table based fractional order composite control scheme for the permanent magnet synchronous motor speed servo system is proposed. Firstly, an extended state observer based comp...

There are very few papers that talk about the global convergence of iterative methods with the help of Banach spaces. The main purpose of this paper is to discuss the global convergence of third order iterative method. The convergence analysis of thi...

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems...

In this paper, we consider the problem of estimating the drift parameters in the mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model. Using the fundamental martingale and the Laplace transform, both the strong...

The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set. In this paper, activated by the consensus of multi-agent systems, the consensus of...

The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities con...

The nonlocal boundary value problem, $d_t^{\rho }u\left(t\right)+Au\left(t\right)=f\left(t\right)$ ($0<\rho <1$, $0<t\le T$), $u\left(\xi \right)=\alpha u\left(0\right)+\phi$ ($\alpha$ is a constant and $0<\xi \le T$), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operato...

Currently, low heat Portland (LHP) cement is widely used in mass concrete structures. The magnesia expansion agent (MgO) can be adopted to reduce the shrinkage of conventional Portland cement-based materials, but very few studies can be found that in...

Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples withou...

Fractional derivatives have been proven to showcase a spectrum of solutions that is useful in the fields of engineering, medical, and manufacturing sciences. Studies on the application of fractional derivatives on fluid flow are relatively new, espec...

The scientific community has recently seen a fast-growing number of publications tackling the topic of fractional-order controllers in general, with a focus on the fractional order PID. Several versions of this controller have been proposed, includin...

This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpecte...

This paper studies the analytical solutions of the fractional fluid models described by the Caputo derivative. We combine the Fourier sine and the Laplace transforms. We analyze the influence of the order of the Caputo derivative the Prandtl number,...

Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathe...

In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fra...

In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition method (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) of fr...

In this paper, two new classes of q-starlike functions in an open unit disc are defined and studied by using the q-fractional derivative. The class $\widetilde{S_q^{*}}\left(\alpha \right)$, $\alpha \in (-3,1]$, $q\in (0,1)$ generalizes the class $S_q^{*}$ of q-starlike f...

The present study focuses on the dynamical aspects of a discrete-time Leslie-Gower predator-prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential...

In this study, a novel design of a second kind of nonlinear Lane–Emden prediction differential singular model (NLE-PDSM) is presented. The numerical solutions of this model were investigated via a neuro-evolution computing intelligent solver us...

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann&...

Nowadays, more and more consumers consider environmentally friendly products in their purchasing decisions. Companies need to adapt to these changes while paying attention to standard business systems such as payment terms. The purpose of this study...

This paper comprehensively reviews the spiral dynamics optimization (SDO) algorithm and investigates its characteristics. SDO algorithm is one of the most straightforward physics-based optimization algorithms and is successfully applied in various br...

In this article, a new method for obtaining closed-form solutions of the simplified modified Camassa-Holm (MCH) equation, a nonlinear fractional partial differential equation, is suggested. The modified Riemann-Liouville fractional derivative and the...

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable $x\in {\mathbb{R}}^n$ and the effect of the coefficient matrices matrices B and C of bou...

The Lieb concavity theorem, successfully solved in the Wigner–Yanase–Dyson conjecture, is an important application of matrix concave functions. Recently, the Thompson–Golden theorem, a corollary of the Lieb concavity theorem, was ex...

Background: solute transport in highly heterogeneous media and even neutron diffusion in nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that solute concent...

The article discusses different schemes for the numerical solution of the fractional Riccati equation with variable coefficients and variable memory, where the fractional derivative is understood in the sense of Gerasimov-Caputo. For a nonlinear frac...

Through direct shear tests, this paper aimed to research the effect of fine marble aggregate on the shear strength and fractal dimension of the interface between soil and concrete corroded by sulfuric acid. More realistic concrete rough surfaces than...

In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and...

We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators and nonnegative singular nonlinearities depending on fractional integrals, supple...

We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions. Using the Riemann–Liouville fracti...

The coupled cubic-quintic nonlinear Schrödinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose–Einstein condensate. In this paper, in order to simplify the process...

In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We...

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Kras...

In this paper, a dissipative version of the Benjamin–Ono dynamics is shown to faithfully model the collective evolution of swarms of scalar Cauchy stochastic agents obeying a follow-the-leader interaction rule. Due to the Hilbert transform, the...

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the ma...

The aim of this paper is to establish the existence and uniqueness results for differential equations of Hilfer-type fractional order with variable coefficient. Firstly, we establish the equivalent Volterra integral equation to an initial value probl...

In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Tayl...

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The...

In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some q-quantum wavelet, is established. A two-parameters exten...

Here, in this article, we investigate the solution of a general family of fractional-order differential equations by using the spectral Tau method in the sense of Liouville–Caputo type fractional derivatives with a linear functional argument. W...

In this article, we construct the exact dynamical wave solutions to the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative by using an efficient and well-established approach, namely: the two-variable $\left(G’/G, \&n\right)$...

This article has a motive to derive a new class of differential equations and associated integral equations for some hybrid families of Laguerre–Gould–Hopper-based Sheffer polynomials. We derive recurrence relations, differential equation...

The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( ${\le }_p$ ). This o...

In the present work, the numerical solution of fractional delay integro-differential equations (FDIDEs) with weakly singular kernels is addressed by designing a Vieta–Fibonacci collocation method. These equations play immense roles in scientifi...

In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type con...

In this study, we depicted the spread of pests in tea plants and their control by biological enemies in the frame of a fractional-order model, and its dynamics are surveyed in terms of boundedness, uniqueness, and the existence of the solutions. To r...